In the past, we have substantially increased the resolution and sensitivity of the technique by introducing diffusional deconvolution techniques to the calculation of sedimentation coefficient distributions. This has become the state-of-the-art of sedimentation velocity analytical ultracentrifugation and is widely applied by research laboratories in this field. Computationally, this method required the solution of the Lamm equation (governing the evolution of the spatial macromolecular concentration profile), and the inversion of an integral equation in conjunction with maximum entropy regularization. Now, we have been able to significantly further increase the resolution of the method by replacing the maximum entropy regularization step with a more general Bayesian analysis. Also, we have developed new finite element solutions of the Lamm equation with significantly higher precision, which will also allow more complex applications in the future. [unreadable] [unreadable] One important application is the study of protein aggregation and fibrillation processes. We have implemented worm-like chain models to provide hydrodynamic scaling laws for the diffusional deconvolution. The detection of trace protein oligomeric species is a topic of great general interest for the study of assembly nucleation events, and of high importance for the detection of immunogenic aggregates in biotechnology. We have exploited the Bayesian analysis tools to specifically enhance the detection of protein oligomers below the 1% limit.